Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 44, Issue 2, 2001, Pages 193-200

  Wang, Jinliang ^a   Chen, Luonan ^b   Jing, Zhujun ^a,c  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b OSAKA SANGYO UNIVERSITY   (Japan)

^c HUNAN NORMAL UNIVERSITY   (China)

Author keywords

Asymptotical stability; Bifurcation; Chaos; Neural network; Snap back repeller

Indexed keywords

EID: 0035245487     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02874421     Document Type: Article

References (11)

1. Hopfield, J., Tank, D., Neural computation of decisions in optimization problems, Biological Cybernetics, 1985, 52: 141.
2. Hopfield, J., Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. USA, 1982, 79: 2554.
3. Chen, L., Aihara, K., Chaotic simulated annealing by a neural network model with transient chaos, Neural Networks, 1995, 8(6): 915.
4. Hopfield, J., Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA, 1984, 81: 3088.
5. Li, J. H., Micheland, A. N., Porod, W., Qualitative analysis and synthesis of a class of neural networks, IEEE Trans. on Circuits and Systems, 1988, 35(8): 976.
6. Gopalsamy, K., He, X. Z., Stability in a symmetric Hopfield nets with transmission delays, Physica D, 1994, 76: 344.
7. Chen, L., Aihara, K., Chaos and asymptotic stability in discrete-time neural networks, Physica D, 1997, 104: 286.
8. Chen, L., Aihara, K., Global searching ability of chaotic neural networks, IEEE Trans. on Circuits and Systems - I: Fundamental Theory and Applications, 1999, 46(8): 974.
9. Tong, H. , Non-linear Time Series - A Dynamical System Approach, Oxford: Oxford University Press, 1990.
10. Hoppensteadt, F., Izhikevich, E., Weakly Connected Neural Networks, New York: Springer-Verlag, 1997.
11. n, J. Math. Anal. Appl., 1978, 63: 199.